Solve sqrt{9(9-3)(9-7)(9-8)}

$$\sqrt{ 9(9-3)(9-7)(9-8) }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Subtract 3 from 9 to get 6.

$$\sqrt{9\times 6\left(9-7\right)\left(9-8\right)}$$

Multiply 9 and 6 to get 54.

$$\sqrt{54\left(9-7\right)\left(9-8\right)}$$

Subtract 7 from 9 to get 2.

$$\sqrt{54\times 2\left(9-8\right)}$$

Multiply 54 and 2 to get 108.

$$\sqrt{108\left(9-8\right)}$$

Subtract 8 from 9 to get 1.

$$\sqrt{108\times 1}$$

Multiply 108 and 1 to get 108.

$$\sqrt{108}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$6\sqrt{3}$$